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Some people ignore weak decks in a multiplayer FFA setting. They believe that because a deck's card quality is poor that leaving that player basically unmolested, and not expending resources to remove that weak player from the game, leaves you with more resources to deal with the stronger decks at the table. Weak decks should be easier to beat when the game comes down to a duel anyway, rather than fighting another strong deck 1 vs 1.

Is there any evidence that weak decks actually win more often than stronger decks played in the same multiplayer FFA setting?

3 Answers
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There's no direct advantage to playing a weaker deck. There is, however, an advantage to managing perceptions.

In some sense, free-for-all is about always being outgunned: taken together, your opponents have more resources — more cards, more mana, more life, more time (turns) — than you do. Luckily, those resources aren't always directed against you at all times. However, as The Ferrett says, "Eventually, you have to be Alpha Threat to win" — and, when you are in that position and most of the table is gunning for you, it pays to have access to strong cards that can power you through that opposition.

Multiplayer strategy writers emphasize the importance of gaming your opponents' perception to get to that point. Your card selection certainly plays a role here:

Even if you're just defending yourself, too powerful of an early board presence might make your opponents see you as the major threat. This could be an argument for playing bad cards, but...

Inversely, too little of an early presence marks you out as an easy target — some players love to take pot shots at anyone who doesn't have some blockers — or, worse yet, gets you flagged as That Guy Biding His Time Until He Can Use His Combo, at which point many players are likely to move to take you out even if you have no obvious strength, based on the fear that you could steal the game at any time.

Some players just love to "spread the love around," e.g. by attacking a different player each round, largely independent of their relative standings. Moreover, lots of multiplayer cards affect all players at the table: you don't have to be "The Threat" to have your carefully-laid plans trampled by another player's Cabal Conditioning. A weaker deck may dodge opponents' direct attention but find its game grinding to a halt anyway because it can't recover from collateral damage.

Thus, depending on the group, appearing weakest may be an advantage, a disadvantage, or largely irrelevant. Strategy writers often advise hiding your strength without actually showing weakness — trying to keep yourself in the "middle of the pack" to avoid the undue attention that may come from being either on top or at the bottom.

In my experience, the best way to dodge attention in multiplayer, particularly with relative strangers (e.g. at a game store rather than an enduring kitchen-table group) is not so much to play a deck that appears weak as a deck that seems linear and predictable. Players tend to spend most of their energy worrying about decks that threaten to do big "broken" game-changing things, or decks whose gameplan they have yet to figure out. Thus, it pays to play a deck that can build up in a slow, measured way with a very "obvious" gameplan, like creature-based midrange beats. Even when opponents notice your buildup, there's a bit of a tendency to dismiss it as a problem they can deal with in a couple more turns, after whatever more pressing concern is addressed.

My wife often steals games this way. She develops her board with some decent creatures, goes after one or two of the weaker players while the big splashy decks fight each other, and then sticks a card like True Conviction or Bellowing Tanglewurm for a game-winning alpha strike once the coast is clear. To win this way, you actually need some of the attributes of a strong deck, just in less "sexy" categories like consistent development and resilience. A deck that's straight-up weak across the board can play the same unassuming startup, but won't be able to capitalize on the late-game state in the same way.

Does her approach win a disproportionate amount of games? It's hard to say with certainty. She seems to win more than her fair share of games, but I do, too, with much splashier punch-everyone-in-the-face control decks. I think trying to be unassuming and predictable works best when there are several big decks fighting for supremacy, e.g. with lock pieces, serving as a suitable distraction for themselves and all of your other opponents; if the table just has one, that deck likely has the resources to run you over while you're still in your "slow and steady" mode.

FFA is a more luck oriented format than 1 vs 1, so of course weak decks will relatively win more than in 1 vs 1. But that doen't really mean that weak decks win more games that strong decks. Also in FFA diplomacy has an important role.

Not all players go first for the strong opponent. There are players that go first for the weak opponents. There are players that go first for strong opponents. There are players that go against nobody and wait for the other players to spend resources fighting between themselves. There are players that go first against opponents who play control decks. There are players with strong decks that form an alliance to defeat the rest of players before fighting between themshelves. There are players with weak decks that form an alliance to defeat first the strong player on the table.

Why is it necessarily more luck-oriented? Arguably FFA multiplayer is more forgiving of players getting stuck with a few bad topdecks, for instance.
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Alex PJun 26 '12 at 23:57

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@user1873 Well, "disproportionate" only has meaning if it's in relation to something else. So I compared it to 1v1. If we only take into account FFA, the it can never be disproportionate: it's the right amount.
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PabloJun 27 '12 at 0:01

@AlexP Luck factor comes from random events. There are two sources of random events in 1v1: two decks. In FFA, there are several, therefore luck becomes more prominent. Also, it's harder to plan ahead in FFA because it's more likely than some of your oponents will have something that break you plans.
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PabloJun 27 '12 at 0:13

@Pablo, disproportionate as compared to strong decks played in multiplayer FFA. If there is no correlation between a weak deck and winning, or a strong deck and winning, you would expect to find a number of wins equal to the number of games played divided by the number of players (I.e. If you play 5 players, you would expect 20% wins. That would be a proportionate win percentage if deck strength had no effect on win percentage. So, do string decks, or weak decks win more on average, or does it have no correlation.)
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user1873Jun 27 '12 at 1:11

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@Pablo I think your luck factor argument is entirely subjective. In 1v1, if you get unlucky, your opponent will take advantage. In FFA this isn't necessarily so, someone else at the table may be in a weaker position so they have been more unlucky, or conversely someone has gotten very lucky and therefore pasted a big target on their forehead.
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ghoppeJun 27 '12 at 15:59

With the people I've played FFA multiplayer the deciding factor of who got attacked wasn't as much about who had the stronger deck but rather who was known as the stronger player. Those who won previous games or were more experienced had a much higher risk of being attacked. Of course smack talk, and other non MtG related things, plays a big role too.

But this is probably more common in playgroups where there's a big difference in experience among the players. Or where the players aren't very competitive, rather just want to have fun.